2024 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Algebra D
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Shou Yoshikawa
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Thu
- Class
- -
- Course Code
- MTH.A404
- Number of credits
- 100
- Course offered
- 2024
- Offered quarter
- 4Q
- Syllabus updated
- Mar 14, 2025
- Language
- English
Syllabus
Course overview and goals
This course follows Advanced topics in Algebra C, building on the topics covered there, we study basic properties and applications of quasi-Frobenius-regularity.
Course description and aims
Students are expected to understand the basic notion of Frobenius regularity and quasi-Frobenius-regularity. Looking through concrete examples and applications, students get acquainted with the fundamental importance of singularities in positive characteristic in current research.
Keywords
Commutative ring, Singularities, Frobenius morphisms, Witt ring.
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Standard lecture course
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Witt ring 1 | Details will be provided during each class session |
| Class 2 | Witt ring 2 | Details will be provided during each class session |
| Class 3 | Quasi-Frobenius splitting | Details will be provided during each class session |
| Class 4 | Quasi-Frobenius splitting for Calabi-Yau varieties | Details will be provided during each class session |
| Class 5 | Fedder type criterion for quasi-Froenius splitting 1 | Details will be provided during each class session |
| Class 6 | Fedder type criterion for quasi-Froenius splitting 2 | Details will be provided during each class session |
| Class 7 | Quasi-Frobenius regularity | Details will be provided during each class session |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to explore references provided in lectures and other materials.
Textbook(s)
None required
Reference books, course materials, etc.
Matsumura, Hideyuki, Commutative ring theory, Cambridge Studies in Advanced Mathematics, 8, 1986.
Karl Schwede, Kevin Tucker, A survey of test ideals, arXiv:1104.2000, 2000.
Evaluation methods and criteria
Course scores are evaluated by homework assignments. Details will be announced during the course.
Related courses
- MTH.A403 ： Advanced topics in Algebra C
Prerequisites
Basic undergraduate algebra in particular commutative ring theory.
Other
None in particular